Question

In triangle MNP, where M, N, and P are the vertices, the side lengths are PM = 8, MN = 23, and PN = 26. Which angle measure appears to be the smallest in triangle MNP? How is it related to the side lengths?

Answer 1

To determine the smallest angle in triangle MNP, we can use the Law of Cosines.

Step-by-step explanation:

To determine the smallest angle in triangle MNP, we can use the Law of Cosines. Let's label the angles of the triangle as ∠N, ∠M, and ∠P, with the corresponding side lengths as MN, NP, and PM. The formula to find the angle is:

cos(∠N) = (NM^2 + NP^2 - PM^2) / (2 * NM * NP)

By plugging in the given side lengths, we can calculate the value of cos(∠N) and then obtain the smallest angle by taking the inverse cosine.